First off, you are told that lines l and n are perpendicular and lines m and n are perpendicular. This means that right angles are created, meaning angle 2 and 8 are 90 degrees.

You are also told that the measure of angle 3 is 54 degrees. The three angles in a triangle add up to 180, so by default the measure of angle 11 is 36 degrees (90+54+x=180). You can verify that this is correct because angle 11 and 7 form a complementary angle, adding up to 90 degrees (54+36=90).

To solve for angle 1 you can subtract angle 2 from 180 (because angles 1 and 2 form a straight line, or supplementary angle, with a 180 degree measure). This means angle 1 is 90 degrees.

To find angle 4 you can do the same as with angle 1, except you use angle 3. Angle 4 ends up being 126 degrees. Angle 6 will also be 126 degrees because of the vertical angle rule. This rule also applies to angle 3 and 5, making angle 5 54 degrees also.

Angle 9 is vertical to angle 11 making angle 9 equal to 36 degrees. Lastly, angle 10 can be solved by subtracting 36 from 180 (because 9 and 10 are supplementary), making angle 10 144 degrees.